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- W2955100823 abstract "We consider elliptic problems with complicated, discontinuous diffusion tensor $A_{scriptscriptstyle 0} $. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say $A_{varepsilon}$, and to use standard finite elements. In cite{Repin2012} a combined modelling-discretization strategy has been proposed which estimates the discretization and modelling errors by a posteriori estimates of functional type. This strategy allows to balance these two errors in a problem adapted way. However, the estimate of the modelling error is derived under the assumption that the difference $A_{scriptscriptstyle 0} -A_{varepsilon}$ is bounded in the $L^{infty}$-norm, which requires that the approximation of the coefficient matches the discontinuities of the original coefficient. Therefore this theory is not appropriate for applications with discontinuous coefficients along textit{complicated, curved} interfaces. Based on bounds for $A_{scriptscriptstyle 0} -A_{varepsilon}$ in an $L^{q}$-norm with $q<infty$ we generalize the combined modelling-discretization strategy to a larger class of coefficients." @default.
- W2955100823 created "2019-07-12" @default.
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- W2955100823 date "2017-04-06" @default.
- W2955100823 modified "2023-10-16" @default.
- W2955100823 title "A Posteriori Modelling-Discretization Error Estimate for Elliptic Problems with L ^infty -Coefficients" @default.
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